An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

ASTiRONOMICAI. P1rOBLEMS. 63.'x. 2. On tlhe 31st of TMarl,:t1816, the sunl's I)e.lination was
ol)scrved at Creelnwichl to be 4f 13' 31'4'" reqllired llis.tight
Ascension, tlhe obliquity of the ecliptic bctng t23' 27' 5 ".
it as, 90 4t7' 5 9"
Ex. 3. Whlat was the suln's Longitudt otl the 28thl of NJovermhel,, lS()) when hlis D)eclination was 2:1~ 16' tt4") and his Rtiglht
AsCeensi on i timel 1O, 1 t1n. 5.8t1 4. 8s.?
Ans. 2s15'~ 39' 10".
Ex. 4. Tlle sun's jLongitude bc)ing 8" 10t' 56", anltd the
ObIlquity 23,3 27' 42}", -what was tthe Rtightt Asctnsiol ill
timel? A-ns. 1611. 23m1. 34s.
1133. (T/I'ven, toe sunt's _lOeti i a /on too fiad! toe time of ~. is.Risn;g a.n/-kd 1l t8t.g, at anyp lace w/w0osd latit(lde.is kao twrn..
Let'E].l't (Fig. 22) represent the meridian of tlm place, Z
being tle zenithl, ai I-d:O() tIhC torizon; and let 1-,' be the a)pparent patlh of tfle sutll ol the l pro- Fig. 22.
posed day, cutting thle horlizon il S.:).I'. -
T'lln t1he arte w;: Z ill l)e thCe!at ituide -
of the place, and consequently El:fI,
or its equal (QO, will be tlhe co-ilatitude, and tllis leastures tlte anglet Ul
)OAQ; also 1{S will be tlie suiln's dee-
lination, and Al\ t expresc-sed in timi1 r
Nwill 1)e thl time of rising befo)re 6 r..
o'leock. 1"or it is evident, thlat it
will. be sunrise wllen tihe stun arrives at the ]torizon at S; but
1:' Ibeting an loutr circle whose )lane is perpcinldictllar to the
meridian (and of course pr)o'cted into a straigltt line on tite
platne of proiection), tli time the suitm is passing from S to 8'
taken firomt the time of describinmg S'1i,, wvhticht is six hlour1s, imust
be thec time from i nidnigltt t to sunrise. I:But the time of describing SS' is measurel'd on the: correspondinl are of the C eqinoetial A1t.:In tlhe ri;t-angled triangle ARS, we have tlte declination
IRS, and thce angle A to find A.:. T. herolfore,
-Rad x xsi~n.A.::::cot A, x tan.IS.
T'x. 1. Required tte time of sunriise at latitude 52~ 13' IN.
w1hen thle sun's declination is 23'28'.